Public Health Minister Rajata Rajatanavin said two laboratories had confirmed the results.
The man has been quarantined at the ministry's infectious diseases facility, he said.
He said the patient was traveling with three other family members, who also are being watched at the facility. Public health officials are also monitoring others who were in contact with the man, including nearby passengers on the airplane.
Rajata said the man didn't have any symptoms while traveling on the plane, but began to have fatigue and difficulty breathing after he was admitted to a private hospital for treatment of his heart condition.
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"We advise the public not to panic because the patient and his family members were separated since the beginning," Rajata said. "Our system is ready and we are monitoring the cases closely."
Thanarath Phalipat, director of the Bureau of Epidemiology, said 59 people who were in contact with the patient have been identified so far by the ministry, including health personnel, hotel employees, passengers who sat two rows in front and behind the patient on the plane, and two taxi drivers.
Middle East respiratory syndrome has killed 23 people and sickened more than 160 in the past month in South Korea, in the biggest outbreak outside the region where it was first seen in 2012. More than 6,700 people are isolated at home or in medical facilities there, according to South Korea's Health Ministry.